Simultaneous Differential Equations

==],k]]n happens that two differential equations are expressed in terms of the same functions. I may be possible to find a single equation in terms of a single function, which may then be solved to find a solution.
We can obtain a single equation in
  by differentiating in (2) and substituting into (1).
From (3)
  then we can write (1) as

This last equation can bee solved using the integrating factor method.
Multiply the equation throughout by
\[e^{\int{-2dx}}= e^{-2x}\]
We obtain
\[f' e^{-2x}-2f e^{-2x}=4e^{-2x} \]
We can rewrite the equation as
Integrate both sides.
\[fe^{-2x}=-2e^{{-2x}}+ C\rightarrow f=-2+Ce^{2x}\]
  then from (2)

You have no rights to post comments